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Highway games on weakly cyclic graphs

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  • Çiftçi, BarIs
  • Borm, Peter
  • Hamers, Herbert

Abstract

A highway problem is determined by a connected graph which provides all potential entry and exit vertices and all possible edges that can be constructed between vertices, a cost function on the edges of the graph and a set of players, each in need of constructing a connection between a specific entry and exit vertex. Mosquera (2007) introduce highway problems and the corresponding cooperative cost games called highway games to address the problem of fair allocation of the construction costs in case the underlying graph is a tree. In this paper, we study the concavity and the balancedness of highway games on weakly cyclic graphs. A graph G is called highway-game concave if for each highway problem in which G is the underlying graph the corresponding highway game is concave. We show that a graph is highway-game concave if and only if it is weakly triangular. Moreover, we prove that highway games on weakly cyclic graphs are balanced.

Suggested Citation

  • Çiftçi, BarIs & Borm, Peter & Hamers, Herbert, 2010. "Highway games on weakly cyclic graphs," European Journal of Operational Research, Elsevier, vol. 204(1), pages 117-124, July.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:1:p:117-124
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    References listed on IDEAS

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    1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    2. Arantza Estévez-Fernández & Peter Borm & Herbert Hamers, 2007. "Project games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 149-176, October.
      • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2005. "Project Games," Other publications TiSEM 21fd9b62-93b6-4a8b-9bf4-4, Tilburg University, School of Economics and Management.
      • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2007. "Project games," Other publications TiSEM 809ba203-2bd2-48ce-ae6d-b, Tilburg University, School of Economics and Management.
      • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2005. "Project Games," Discussion Paper 2005-91, Tilburg University, Center for Economic Research.
    3. Granot, D. & Hamers, H.J.M. & Tijs, S.H., 1999. "On some balanced, totally balanced and submodular delivery games," Other publications TiSEM e0496604-0162-4a27-992c-a, Tilburg University, School of Economics and Management.
    4. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    5. Potters, J.A.M. & Curiel, I. & Tijs, S.H., 1992. "Traveling salesman games," Other publications TiSEM 0dd4cf3d-25fa-4179-80f6-6, Tilburg University, School of Economics and Management.
    6. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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    Cited by:

    1. Balázs Sziklai & Tamás Fleiner & Tamás Solymosi, 2014. "On the Core of Directed Acyclic Graph Games," CERS-IE WORKING PAPERS 1418, Institute of Economics, Centre for Economic and Regional Studies.
    2. Kuipers, Jeroen & Mosquera, Manuel A. & Zarzuelo, José M., 2013. "Sharing costs in highways: A game theoretic approach," European Journal of Operational Research, Elsevier, vol. 228(1), pages 158-168.
    3. Herbert Hamers & Nayat Horozoglu & Henk Norde & Trine Tornøe Platz, 2022. "On the properties of weighted minimum colouring games," Annals of Operations Research, Springer, vol. 318(2), pages 963-983, November.
    4. Sanjith Gopalakrishnan & Daniel Granot & Frieda Granot & Greys Sošić & Hailong Cui, 2021. "Incentives and Emission Responsibility Allocation in Supply Chains," Management Science, INFORMS, vol. 67(7), pages 4172-4190, July.
    5. Gómez-Rodríguez, Marcos & Davila-Pena, Laura & Casas-Méndez, Balbina, 2024. "Cost allocation problems on highways with grouped users," European Journal of Operational Research, Elsevier, vol. 316(2), pages 667-679.
    6. Hamers, Herbert & Horozoglu, Nayat & Norde, Henk & Platz, Trine Tornoe, 2022. "On the properties of weighted minimum colouring games," Other publications TiSEM ee84d5e4-08d7-4154-9521-2, Tilburg University, School of Economics and Management.
    7. repec:has:discpr:1321 is not listed on IDEAS
    8. Sudhölter, Peter & Zarzuelo, José M., 2017. "Characterizations of highway toll pricing methods," European Journal of Operational Research, Elsevier, vol. 260(1), pages 161-170.

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    More about this item

    Keywords

    C71 Cooperative games Highway games Cost sharing;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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